An atomic force microscope (AFM) is an apparatus for measuring the force which interacts between a probe with a sharp tip and a sample surface from the displacement of a cantilever, and one-dimensionally or two-dimensionally scanning the sample surface with the probe to obtain the sample surface's information, e.g. its geometry. One known type of AFM is an FM-AFM with a frequency modulation detection system. In an FM-AFM, a cantilever holding a probe approximate to the distance from the sample surface at the atomic level is oscillated with the mechanical resonance frequency, and the resonance frequency's variation (or frequency shift Δf) is detected which is caused by the interaction force acting between the probe and the sample surface. Since the frequency shift Δf depends on the distance Z between the probe and the sample surface, by performing a two-dimensional scan (e.g. raster scan) of the sample surface in a plane orthogonal to the normal direction on the sample while keeping the frequency shift Δf constant, a concave-convex observation image (or Δf constant image) of the sample surface can be obtained.
Although it is possible to obtain much information from the interaction force between the probe and the sample surface as will be described later, an FM-AFM has a disadvantage in that the interaction force cannot be directly and experimentally obtained. Therefore, the relationship (which will be hereinafter called a “Δf curve”) between the frequency shift Δf and the probe-sample surface distance Z is measured as previously described, and a conversion calculation based on a theory described in Non-Patent Documents 1 through 3 for example is performed to obtain the relationship between the interaction force F and the probe-sample surface distance Z (which will be hereinafter called an “F curve”). In addition, using the relationship that the interaction force F is a potential gradient, the potential energy curve between the probe and the sample surface can also be deduced from the F curve.
Roughly speaking, the interaction force between the probe and the sample surface consists of a long-range interaction force (FLR: Long-Range Force) which mainly acts when the distance Z is within a range from a few nm to several tens of nm, and a short-range interaction force (FSR: Short-Range Force) which acts when the distance Z is as small as 1 nm or less. The sum of these forces acts as a total interaction force (Ftotal: Total Force). The long-range interaction force FLR includes for example a van der Waals force Fvdw between the probe and the sample surface, and an electrostatic force Fele caused by the contact potential difference between the probe and the sample surface. On the other hand, an example of the short-range interaction force FSR is a covalent force that acts between semiconductor atoms. It is known that the short-range interaction force FSR not only contributes to the sample surface's concave-convex observation at the atomic resolution, but reflects the atomic-level configuration of the tip of the probe (refer to Non-Patent Document 4). Moreover, it has been reported that the difference in the short-range interaction force FSR of the atomic species can be utilized for the atomic species' identification (refer to Non-Patent Document 5).
Therefore, in order to obtain various pieces of information about a sample at the atomic level, the technique of accurately measuring the short-range interaction force FSR has been recently required. A conventional and general procedure (refer to Non-Patent Document 6) for measuring, by using an atomic force microscope, the short-range interaction force FSR acting on a target atom existing on the sample surface will now be schematically explained. FIG. 14 is a flowchart illustrating this procedure, and FIG. 15 is a graph illustrating an example of the Δf curve and F curve.
First, the contact potential difference between the probe and the sample surface is measured, and a bias voltage which compensates this contact potential difference is applied between the probe and the sample surface to make the electrostatic force Fele negligible (Step S11). Since the van der Waals force Fvdw and the electrostatic force Fele are dominant in the long-range interaction force FLR, in the state where the electrostatic force Fele is negligible, the van der Waals force Fvdw can be regarded as the only dominant component.
Next, using the atomic force microscope, a Δf curve is obtained on an atomic defect (or Defect), where only the long-range interaction force FLR acts between the probe and the sample surface. As illustrated in FIG. 15(a), a Δf curve is a graph with the probe-sample surface distance Z assigned to the horizontal axis and the frequency shift Δf to the longitudinal axis. In the case where the interaction force acting between the probe and the sample surface is an attracting force, the frequency shift Δf becomes a negative value and asymptotically gets closer to zero as the distance Z increases. The Δf curve on the atomic defect is labeled as the ΔfDefect curve (Step S12). The position of the atomic defect can be visually recognized on the FM-AFM concave-convex observation image of the sample surface. At this point in time, in order to apply the conversion theory from the Δf curve into F curve as described in Non-Patent Document 2 for example, it is required to measure the Δf curve over a distance range that is large enough for the frequency shift Δf to become substantially zero. Generally, this distance is approximately several tens of nm.
A conversion computation from the frequency shift Δf into the interaction force F is performed based on the aforementioned, publicly known conversion theory, whereby the FDefect curve which illustrates the relationship between the interaction force and the probe-sample surface distance Z on the atomic defect is obtained from the ΔfDefect curve (Step S13). As illustrated in FIG. 15(b), an F curve is a graph with the probe-sample surface distance Z assigned to the horizontal axis and the interaction force F to the longitudinal axis.
Using a van der Waals force model or the like in which the sample surface is assumed to be flat and the tip of the probe spherical, a fitting is performed to the FDefect curve to check the validity of the assumed model. This process determines the fitting curve of the long-range interaction force FLR (Step S14). In practice, however, in the case where the objective is to obtain only the long-range interaction force FLR, it is not necessary to obtain the fitting curve of the long-range interaction force FLR but the FDefect curve may be directly used.
Subsequently, using the atomic force microscope, a Δf curve is obtained on the target atom. This Δf curve reflects both the short-range interaction force FSR and the long-range interaction force FLR. The Δf curve is labeled as the ΔfAtom curve (Step S15). The position of the target atom can also be determined from the FM-AFM concave-convex observation image of the sample surface. This ΔfAtom curve also requires the measurement of the range up to approximately several tens of nm as in the case of the ΔfDefect curve.
As in Step S13, a conversion from the frequency shift Δf into the interaction force F is performed based on the conversion theory, whereby the FAtom curve which illustrates the relationship between the interaction force and the probe-sample surface distance Z on the target atom is obtained from the ΔfAtom curve (Step S16).
Since the FAtom curve reflects the sum of the long-range interaction force and the short-range interaction force, an FSR curve is computed by subtracting the fitting curve of the long-range interaction force FLR which has been obtained in Step S14 from the FAtom curve (or by subtracting FDefect curve). From this FSR curve, the short-range interaction force FSR on the target atom is obtained (Step S17).
However, the aforementioned conventional method for computing the short-range interaction force FSR has some problems as follows.
(1) Generally, the contact potential difference between the semiconductor surface and a silicon probe for example is approximately within ±1V. In Step S11, an appropriate bias voltage which corresponds to this voltage is applied between the probe and the sample surface to experimentally minimize the electrostatic force Fele. However, applying this bias voltage does not always make the electrostatic force Fele completely zero, whose effect may not be negligible and decrease the accuracy. In addition, in the case of an insulator sample such as an ionic crystal, the compensation of the contact potential difference is virtually impossible since it is difficult to apply a bias voltage between the probe's tip and the sample surface.
(2) In many FM-AFMs, a piezoelectric element is used for controlling the microscopic distance between the probe and the sample surface. In such a case, it is necessary to significantly change the applied voltage to the piezoelectric element to obtain a Δf curve with a long range scale. This might cause the piezoelectric element's creep (i.e. a phenomenon in which a gradual displacement occurs even while the applied voltage is kept constant), which causes concern about the accuracy decrease of the position control. In addition, since the acquisition of a Δf curve with a long range scale requires a long measurement time, the effect of the drift of the probe-sample surface distance due to the thermal expansion of the probe or sample becomes prominent. Therefore, the range scale for measuring the Δf curve should preferably be as short as possible.
(3) In performing the conversion from a Δf curve into an F curve using the method described in Non-Patent Document 2, a few through several tens of minutes' computational time is required, depending on the computing speed of the computer. For example, with a workstation with a Xeon 3 GHz dual processor produced by Intel Corporation in the United States, the conversion from a Δf curve with one thousand and twenty four points into an F curve requires more than five minutes. With the aforementioned conventional method, this time-consuming computation must be performed two times, i.e. in Steps S13 and S16, which further elongates the analysis time. In particular, although obtaining the short-range interaction force of only one point poses no problem, obtaining the short-range interaction force of a plurality of points takes an impractically long period of time.    [Non-Patent Document 1] U. Durig, “Extracting interaction forces and complementary observables in dynamic probe microscopy,” Applied Physics Letters, vol. 76 (2000), pp. 1203-1205    [Non-Patent Document 2] F. J. Giessibl, “A direct method to calculate tip-sample forces from frequency shifts in frequency-modulation atomic force microscopy,” Applied Physics Letters, vol. 78 (2001), pp. 123-125    [Non-Patent Document 3] John E. Sader et al., “Accurate formulas for interaction force and energy in frequency modulation force spectroscopy,” Applied Physics Letters, vol. 84 (2004), pp. 1801-1803    [Non-Patent Document 4] Noriaki Oyabu et al., “Single Atomic Contact Adhesion and Dissipation in Dynamic Force Microscopy,” Physical Review Letters, vol. 96 (2006), pp. 106101-1 through 106101-4    [Non-Patent Document 5] Yoshiaki Sugimoto et al., “Real topography, atomic relaxations, and short-range chemical interactions in atomic force microscopy: The case of the α-Sn/Si(111)-(√3×√3)R30° surface,” Physical Review B, vol. 73 (2006), pp. 205329-1 through 205329-9    [Non-Patent Document 6] M. A. Lantz et al., “Quantitative Measurement of Short-Range Chemical Bonding Forces,” Science, vol. 291 (2001), pp. 2580-2583